Q. $\int_{2}^{3}\frac{dx}{x^{2} - x}$ is equal to
A) $\log\left( \frac{2}{3} \right)$
B) $\log\left( \frac{1}{4} \right)$
C) $\log\left( \frac{4}{3} \right)$
D) $\log\left( \frac{8}{3} \right)$
Explanation
(c)
$\int_{2}^{3}\frac{dx}{x^{2} - x}$
$= \int_{2}^{3}{\frac{dx}{x(x - 1)} = \int_{2}^{3}{\left\lbrack \frac{1}{x - 1} - \frac{1}{x} \right\rbrack dx}}$
$= \lbrack{\log{(x - 1)\rbrack}}_{2}^{3} - \lbrack{\log{x\rbrack}}_{2}^{3}$
$= \lbrack\log{2 - \log{1\rbrack - \lbrack\log{3 - \log{2\rbrack}}}}$
$= 2\log{2 - \log{3 = \log\frac{4}{3}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.